gap> h:=[];
[  ]
gap> 
gap> h[1]:=();
()
gap> h[2]:=(1,24)(2,13)(3,14)(4,15)(5,16)(6,17)(7,18)(8,19)*
> (9,20)(10,21)(11,22)(12,23);
( 1,24)( 2,13)( 3,14)( 4,15)( 5,16)( 6,17)( 7,18)( 8,19)( 9,20)(10,21)(11,22)
(12,23)
gap> h[3]:=(2,3,4,5,6,7,8,9,10,11,12)*
> (13,14,15,16,17,18,19,20,21,22,23);
( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)
gap> h[4]:=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23);
( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)
gap> h[5]:=(24,21,20,13,19,5,23,3,18,16,6,9,22,14,4,2,17,8,15,12,7,11,10);
( 2,17, 8,15,12, 7,11,10,24,21,20,13,19, 5,23, 3,18,16, 6, 9,22,14, 4)
gap> h[6]:=(2,3,4,5,6,7,8,9,10,11,12)*
> (13,14,15,16,17,18,19,20,21,22,23)^-1;
( 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)(13,23,22,21,20,19,18,17,16,15,14)
gap> h[7]:=(4,8,9,12,10)(7,6,3,5,11)(15,19,20,23,21)(18,17,14,16,22);
( 3, 5,11, 7, 6)( 4, 8, 9,12,10)(14,16,22,18,17)(15,19,20,23,21)
gap> h[8]:=(1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24);
( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24)
gap> h[9]:=(1,2,3,4,5,6,7,8,9,10,11,12)*
> (13,14,15,16,17,18,19,20,21,22,23,24)^-1;
( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12)(13,24,23,22,21,20,19,18,17,16,15,14)
gap> 
gap> #H:=Group(h[1],h[2],h[6],h[7],h[8]);
gap> 
gap> M23:=Group(h[5],h[7]);
Group( ( 2,17, 8,15,12, 7,11,10,24,21,20,13,19, 5,23, 3,18,16, 6, 9,22,14, 4
 ), ( 3, 5,11, 7, 6)( 4, 8, 9,12,10)(14,16,22,18,17)(15,19,20,23,21) )
gap> F2:= FreeGroup( "a", "b");
Group( a, b )
gap> words := [ F2.1, F2.2 ];
[ a, b ]
gap> P := PresentationViaCosetTable(M23,F2,words);